Problem: What is $\vec a + \vec b$ ? $\begin{align*} \vec a &= 4 \hat\imath - 3 \hat\jmath \\ \vec b &= -8 \hat\imath - 4 \hat\jmath \end{align*}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ $\vec a$ $\vec b$
Answer: Sum the $\hat\imath$ and $\hat\jmath$ components separately. $\vec a + \vec b = (4 - 8) \hat\imath + (-3 - 4) \hat\jmath$ $\hphantom{\vec a + \vec b} = -4\hat\imath - 7\hat\jmath$